Given a Bayesian network as shown below,

Fill in the following blanks.

The probability of the alarm sounding when there is neither a burglary nor an earthquake is [blank1] (keep three decimal places).

Question

Given a Bayesian network as shown below,

Fill in the following blanks.

The probability of the alarm sounding when there is neither  a burglary nor an earthquake is [blank1] (keep three decimal places).

BlackTom AI · Accepted Answer

To approach this question, first identify the structure of the Bayesian network: the alarm A depends on B (Burglary) and E (Earthquake), and there are conditional probabilities P(A | B, E) provided for each combination of B and E being true or false. The task is to find P(A = true | B = false, E = false), i.e., the probability the alarm sounds when neither burglary nor earthquake occurs.

Step 1: Note the relevant conditional probability table for A given B and E. From the diagram, the values are:
- P(A = true | B = true, E = true) = 0.95
- P(A = true | B = true, E = false) = 0.94
- P(A = true | B = false, E = true) = 0.29
- P(A = true | B = false, E = false) = 0.001
These entries show that the alarm’s probability is highly dependent on whether burglary and earthquake occur, and very small when both are absent.

Step 2: Apply the given condition B = false and E = false. This corresponds to the last row of the conditional probability table: B = f, E = f.
Thus, P(A = true | B = false, E = false) = 0.001.

Step 3: Present the result with the requested precision. Since the problem asks to keep three decimal places, we report 0.001.

Rationale for why this is correct and why other contextual cases would differ: The network explicitly encodes A as a child of B and E, with a specific conditional probability for each combination of B and E. When both parents are false, the probability of A being true is the value associated with that combination in the table. If either B or E were true, we would use the corresponding row (e.g., B = true, E = false yields 0.94; B = false, E = true yields 0.29; both true yields 0.95). The calculations do not involve any additional factors such as priors for B or E in this conditional probability query because the question conditions on B and E being false.

42172 Introduction to Artificial Intelligence - Spring 2025 Lec11 class quiz

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the alarm sounding when there is neither a burglary nor an earthquake is [blank1] (keep three decimal places).

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